2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62339We prove that, for every decreasing sequence {a \sb k} of natural numbers, there exists a map f: X --> X with cat (f\sp k)=a\sb k.LATEX, 3 pages, minor changesAlgebraic TopologyOn sequences cat (f\sp k)text